Just because green shoots appear doesn't mean they have to grow very fast.

Look at US unemployment. Signs keep popping up that it's getting worse less quickly. First-time claims for jobless benefits fell by 4,000 last week to 570,000, the US Department of Labor reported Thursday. But that "fall" occurred because the US Department of Labor revised upward the previous week by – can you guess? – 4,000.

The end result: The official number of Americans drawing unemployment benefits reported Thursday was the same as the official number reported last week. The closely watched four-week average of first-time claims actually went up to remain at its highest level since mid-July.

Friday's unemployment figures for August should provide further clarity. But the signs so far suggest that the pace of the deterioration of the labor market, while much less rapid than six months ago, is not slackening as quickly as many expected. (Click here for a look at how small business has become the biggest source of layoffs.)

"The labor market’s healing process is agonizingly slow," writes Joshua Shapiro, an economist with MFR Inc., in an analysis. "We expect the improvement to remain a very slow one."

A more positive sign emerged Thursday from the Monster.com's monthly index of online job offerings. The index of job availability rose 6 percent from July to August, its fastest rate of increase in four years. Still, the index remained 24 percent below last August's reading.